Question

if the equation 2x square + kx - 5 = 0 and x square - 3 x minus 4 is equal zero have one root in common then find the value of k

Answer 1

Step-by-step explanation:

Given that the equations 2x² + kx - 5 = 0 and x² - 3x - 4 have one common root.

Let the common root be y.

Substitute the value of y, we get

2y² + ky - 5 = 0

y² - 3y - 4 = 0

On solving (i) & (ii) * 2, we get

2y² + ky = 5

2y² - 6y = 8

-----------------------

       (k + 6)y = -3

        y = -3/k + 6

Substitute y in (i), we get

⇒ 2y² + ky - 5 = 0

⇒ 2(-3/k + 6)² + k(-3/k + 6) - 5 = 0

⇒ 18 - 3k(k + 6) = 5(k + 6)²

⇒ 18 - 3k² - 18k = 5(k² + 36 + 12)

⇒ -8k² - 78k - 162 = 0

⇒ 8k² + 78k + 162 = 0

⇒ 4k² + 39k + 81 = 0

⇒ 4k² + 12k + 27k + 81 = 0

⇒ 4k(k + 3) + 27(k + 3) = 0

⇒ (k + 3)(4k + 27) = 0

⇒ k = -3, -27/4

Hope it helps!

Answer 2

2x^2+kx-5=0.........(1)

x^2-3x-4=0..........(2)

solving equation 2

x^2-3x+x-4=0;

(x+1)(x-4)=0;

x=-1;x=4;

put x value in first equation

x=-1;

2-k-5=0;

k=-3;

x=4;

32+4k-5=0

k=-27/4